Final answer:
To find the height above the surface of the Earth where the acceleration due to gravity is reduced to 90% of its surface value, we can use the formula for gravitational acceleration.
Step-by-step explanation:
To find the height above the surface of the Earth where the acceleration due to gravity is reduced to 90% of its surface value, we can use the formula for gravitational acceleration:
g = (G * M) / r^2
where g is the acceleration due to gravity, G is the gravitational constant, M is the mass of the Earth, and r is the distance from the center of the Earth.
Given that the radius of the Earth is 6378 km, the surface value of the gravitational acceleration can be found using the formula above. Then we can use a proportion to find the height where the acceleration is reduced to 90% of its surface value.
The question asks at what altitude above the Earth's surface is the acceleration due to gravity (g) decreased to 90% of its surface value, given that the radius of the Earth is 6378 km. To solve this problem, we need to use Newton's Universal Law of Gravitation and the formula for the acceleration due to gravity at a distance r from the center of the Earth, which is g = G * M / r², where G is the gravitational constant, M is the mass of the Earth, and r is the distance from the Earth's center.
Since we are looking for 90% of the surface gravity, we set the equation to 0.9g = G * M / (R+h)², where R is the Earth's radius (6378 km) and h is the altitude above the Earth's surface where gravity is 90% of its surface value. Solving for h will give us the required altitude. To solve this, we can rearrange the equation to find h and then plug in the known values for R and g.